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人気のある微分積分 >

integral from 0 to 1 of xe^x-(e^{2x})/2

解

\int_{0}^{1} x e^{x} - \frac{e ^{2 x}}{2} d x

解

1 - \frac{e ^{2} - 1}{4}

+1

十進法表記

- 0.59726 \dots

解答ステップ

\int_{0}^{1} x e^{x} - \frac{e ^{2 x}}{2} d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} x e^{x} d x - \int_{0}^{1} \frac{e ^{2 x}}{2} d x

\int_{0}^{1} x e^{x} d x = 1

\int_{0}^{1} \frac{e ^{2 x}}{2} d x = \frac{e ^{2} - 1}{4}

= 1 - \frac{e ^{2} - 1}{4}

グラフ

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